Question

$ \underset{x\to 0}{\mathop{\lim }}\,\left( \frac{{{a}^{x}}-{{b}^{x}}}{x} \right) $ is equal to:

• A. 0
• B. 1
• C. $ log\text{ }a-log\text{ }b $
• D. $ log\text{ }a/log\text{ }b $
• E. does not exist

Answer 1

Answer: (C)

$ \underset{x\to 0}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{b}^{x}}}{x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{a}^{x}}-x}{x}-\underset{x\to 0}{\mathop{\lim }}\,\frac{{{b}^{x}}-1}{x} $